#root(3)(25x^11)/root(3)(9w^2)#
we need to rationalize the denominator first.
What we are looking for are factors that are multiples of the index, or perfect cubes.
#root(3)(25x^11)/root(3)(9w^2)#
#9 * 3 = 27# meaning #3^3# is 27
#w^2 *w = w^3# giving us another perfect cube rationalizing the denominator
#root(3)(25x^11)/root(3)(9w^2)*root(3)(3w)/root(3)(3w) = (root(3)125 root(3)(w)root(3)(x^11))/(root(3)(27w^3)#
In the numerator:
#root(3)125 = 5 # Is a perfect cube
#root(3)w# is fully simplified
#root(3)x^9# #* root(3)x^2 = root(3)x^11#
#x^(9/3)# = # x^3#
#root(3)27# #root(3) w^3# This is the denominator
#root(3)27 = 3 #
#root(3)w^3 = w#
put it all back together over a single fraction
#(5x^3 root(3)(x^2)root(3)w)/(3w)#
